简介
Summary:
Publisher Summary 1
In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on "Quasiconformal mappings and analysis" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.
Publisher Summary 2
This book comprises a broad selection of expository articles that were written in conjunction with an international conference held to honor F.W. Gehring on the occasion of his 70th birthday. The objective of both the symposium and the present volume was to survey a wide array of topics related to Gehring's fundamental research in the field of quasiconformal mappings, emphasizing the relation of these mappings to other areas of analysis. The book begins with a short biographical sketch and an overview of Gehring's mathematical achievements, including a complete list of his publications. This is followed by Olli Lehto's account of Gehring's career-long involvement with the Finnish mathematical community and his role in the evolution of the Finnish school of quasiconformal mapping. The remaining articles, written by prominent authorities in diverse branches of analysis, are arranged alphabetically. The principal speakers at the symposium were: Astala, Baernstein Earle, Jones, Kra, Lehto, Martin, Sullivan, and Va"isa"la". Other individuals, some unable to attend the conference, were invited to contribute articles to the volume, which should give readers new insights into numerous aspects of quasiconformal mappings and their applications to other fields of mathematical analysis. Friends and colleagues of Professor Gehring will be especially interested in the personal accounts of his mathematical career and the descriptions of his many important research contributions.
目录
Table Of Contents:
Preface vii
F.W. Gehring: A Biographical Sketch 1(4)
Peter Duren
The Mathematics of F.W. Gehring 5(4)
Juha Heinonen
Bruce Palka
Publications of F.W. Gehring 9(8)
Ph.D. Students of F.W. Gehring 17(2)
Fred Gehring and Finnish Mathematics 19(14)
Olli Lehto
Planar Quasiconformal Mappings; Deformations and Interactions 33(22)
Kari Astala
Local Minimality Results Related to the Bloch and Landau Constants 55(36)
Albert Baernstein II
Jade P. Vinson
The Apollonian Metric of a Domain in R(n) 91(18)
A.F. Beardon
Conjugacy Invariants of Mobius Groups 109(32)
C. Cao
P.L. Waterman
Extremal Quasiconformal Mappings in Plane Domains 141(18)
Clifford J. Earle
Li Zhong
On the Asymptotic Behavior of Quasiconformal Mappings in Space 159(22)
V. Ya. Gutlyanskii
O. Martio
V.I. Ryazanov
M. Vuorinen
The Gehring Lemma 181(24)
Tadeusz Iwaniec
Old and New on the Quasihyperbolic Metric 205(16)
Pekka Koskela
Kleinian Groups; Eichler Cohomology and the Complex Theory 221(32)
Irwin Kra
On the Geometry of Kleinian Groups 253(22)
Gaven J. Martin
Old and New on the Schwarzian Derivative 275(34)
Brad Osgood
The Gehring-Hayman Inequality in Conformal Mapping 309(12)
Ch. Pommerenke
S. Rohde
Extremal Extensions from the Circle to the Disk 321(16)
Edgar Reich
Construction of Quasiregular Mappings 337(10)
Seppo Rickman
Mappings and Spaces 347(22)
Stephen Semmes
Questions on Quasiconformal Maps in Space 369(6)
Jussi Vaisala
List of Contributors 375
Preface vii
F.W. Gehring: A Biographical Sketch 1(4)
Peter Duren
The Mathematics of F.W. Gehring 5(4)
Juha Heinonen
Bruce Palka
Publications of F.W. Gehring 9(8)
Ph.D. Students of F.W. Gehring 17(2)
Fred Gehring and Finnish Mathematics 19(14)
Olli Lehto
Planar Quasiconformal Mappings; Deformations and Interactions 33(22)
Kari Astala
Local Minimality Results Related to the Bloch and Landau Constants 55(36)
Albert Baernstein II
Jade P. Vinson
The Apollonian Metric of a Domain in R(n) 91(18)
A.F. Beardon
Conjugacy Invariants of Mobius Groups 109(32)
C. Cao
P.L. Waterman
Extremal Quasiconformal Mappings in Plane Domains 141(18)
Clifford J. Earle
Li Zhong
On the Asymptotic Behavior of Quasiconformal Mappings in Space 159(22)
V. Ya. Gutlyanskii
O. Martio
V.I. Ryazanov
M. Vuorinen
The Gehring Lemma 181(24)
Tadeusz Iwaniec
Old and New on the Quasihyperbolic Metric 205(16)
Pekka Koskela
Kleinian Groups; Eichler Cohomology and the Complex Theory 221(32)
Irwin Kra
On the Geometry of Kleinian Groups 253(22)
Gaven J. Martin
Old and New on the Schwarzian Derivative 275(34)
Brad Osgood
The Gehring-Hayman Inequality in Conformal Mapping 309(12)
Ch. Pommerenke
S. Rohde
Extremal Extensions from the Circle to the Disk 321(16)
Edgar Reich
Construction of Quasiregular Mappings 337(10)
Seppo Rickman
Mappings and Spaces 347(22)
Stephen Semmes
Questions on Quasiconformal Maps in Space 369(6)
Jussi Vaisala
List of Contributors 375
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